On the symmetric Laplace derivative

A. Garai; S. Ray

doi:10.1007/s10474-011-0110-6

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Acta Mathematica Hungarica

Volume/Issue:: Volume 133: Issue 1-2

On the symmetric Laplace derivative

Authors: A. Garai¹ and S. Ray²

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¹ Memari College, Memari, Burdwan, West Bengal, India
² Department of Mathematics, Visva-Bharati University, Santiniketan, West Bengal, India

DOI:: https://doi.org/10.1007/s10474-011-0110-6

Page Count:: 166–184

Publication Date:: 01 Oct 2011

Online Publication Date:: 19 May 2011

Article Category:: Research Article

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Abstract

Let f: R→R be integrable in a neighbourhood of x∊R. If there are real numbers α₀,α₂,…,α_2n−2 such that

exists for some δ>0 then the limit is called the 2n-th symmetric Laplace derivative at x. There is a corresponding definition of (2n+1)-th symmetric Laplace derivative. It is shown that this derivative is a generalization of the symmetric d.l.V.P. derivative. Some properties of this derivative are studied.